TSTP Solution File: LCL535+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL535+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:48:19 EDT 2023
% Result : Theorem 28.81s 13.86s
% Output : CNFRefutation 28.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 206
% Syntax : Number of formulae : 365 ( 120 unt; 163 typ; 0 def)
% Number of atoms : 302 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 184 ( 84 ~; 70 |; 2 &)
% ( 18 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 62 ( 60 usr; 60 prp; 0-2 aty)
% Number of functors : 103 ( 103 usr; 94 con; 0-2 aty)
% Number of variables : 200 (; 200 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > strict_implies > strict_equiv > or > implies > equiv > and > #nlpp > possibly > not > necessarily > substitution_strict_equiv > substitution_of_equivalents > r5 > r4 > r3 > r2 > r1 > or_3 > or_2 > or_1 > op_strict_implies > op_strict_equiv > op_possibly > op_or > op_necessarily > op_implies_or > op_implies_and > op_implies > op_equiv > op_and > necessitation > modus_tollens > modus_ponens_strict_implies > modus_ponens > kn3 > kn2 > kn1 > implies_3 > implies_2 > implies_1 > equivalence_3 > equivalence_2 > equivalence_1 > cn3 > cn2 > cn1 > axiom_s4 > axiom_s3 > axiom_s2 > axiom_s1 > axiom_m9 > axiom_m8 > axiom_m7 > axiom_m6 > axiom_m5 > axiom_m4 > axiom_m3 > axiom_m2 > axiom_m10 > axiom_m1 > axiom_M > axiom_K > axiom_B > axiom_5 > axiom_4 > and_3 > and_2 > and_1 > adjunction > #skF_33 > #skF_41 > #skF_60 > #skF_57 > #skF_52 > #skF_76 > #skF_67 > #skF_49 > #skF_20 > #skF_18 > #skF_17 > #skF_78 > #skF_94 > #skF_11 > #skF_86 > #skF_31 > #skF_15 > #skF_69 > #skF_25 > #skF_55 > #skF_87 > #skF_38 > #skF_36 > #skF_80 > #skF_56 > #skF_54 > #skF_43 > #skF_79 > #skF_19 > #skF_40 > #skF_48 > #skF_7 > #skF_37 > #skF_71 > #skF_10 > #skF_16 > #skF_85 > #skF_47 > #skF_92 > #skF_65 > #skF_26 > #skF_81 > #skF_53 > #skF_14 > #skF_51 > #skF_5 > #skF_45 > #skF_46 > #skF_39 > #skF_72 > #skF_6 > #skF_13 > #skF_61 > #skF_2 > #skF_68 > #skF_82 > #skF_84 > #skF_3 > #skF_1 > #skF_89 > #skF_21 > #skF_9 > #skF_32 > #skF_64 > #skF_50 > #skF_90 > #skF_8 > #skF_30 > #skF_42 > #skF_77 > #skF_4 > #skF_22 > #skF_93 > #skF_29 > #skF_28 > #skF_35 > #skF_70 > #skF_66 > #skF_24 > #skF_27 > #skF_23 > #skF_63 > #skF_88 > #skF_44 > #skF_83 > #skF_59 > #skF_73 > #skF_91 > #skF_58 > #skF_12 > #skF_62 > #skF_34 > #skF_75 > #skF_74
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(implies_2,type,
implies_2: $o ).
tff(r1,type,
r1: $o ).
tff(axiom_s1,type,
axiom_s1: $o ).
tff(equiv,type,
equiv: ( $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': $i ).
tff('#skF_41',type,
'#skF_41': $i ).
tff(r3,type,
r3: $o ).
tff('#skF_60',type,
'#skF_60': $i ).
tff(op_possibly,type,
op_possibly: $o ).
tff('#skF_57',type,
'#skF_57': $i ).
tff('#skF_52',type,
'#skF_52': $i ).
tff(equivalence_2,type,
equivalence_2: $o ).
tff('#skF_76',type,
'#skF_76': $i ).
tff(axiom_m8,type,
axiom_m8: $o ).
tff('#skF_67',type,
'#skF_67': $i ).
tff('#skF_49',type,
'#skF_49': $i ).
tff(and_2,type,
and_2: $o ).
tff(axiom_4,type,
axiom_4: $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff(op_implies_or,type,
op_implies_or: $o ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_78',type,
'#skF_78': $i ).
tff(adjunction,type,
adjunction: $o ).
tff('#skF_94',type,
'#skF_94': $i ).
tff(r5,type,
r5: $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(kn3,type,
kn3: $o ).
tff('#skF_86',type,
'#skF_86': $i ).
tff('#skF_31',type,
'#skF_31': $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_69',type,
'#skF_69': $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(axiom_m3,type,
axiom_m3: $o ).
tff(cn2,type,
cn2: $o ).
tff(axiom_K,type,
axiom_K: $o ).
tff('#skF_55',type,
'#skF_55': $i ).
tff('#skF_87',type,
'#skF_87': $i ).
tff(possibly,type,
possibly: $i > $i ).
tff(r4,type,
r4: $o ).
tff('#skF_38',type,
'#skF_38': $i ).
tff('#skF_36',type,
'#skF_36': $i ).
tff('#skF_80',type,
'#skF_80': $i ).
tff(axiom_B,type,
axiom_B: $o ).
tff('#skF_56',type,
'#skF_56': $i ).
tff(op_strict_equiv,type,
op_strict_equiv: $o ).
tff('#skF_54',type,
'#skF_54': $i ).
tff(axiom_5,type,
axiom_5: $o ).
tff('#skF_43',type,
'#skF_43': $i ).
tff('#skF_79',type,
'#skF_79': $i ).
tff(op_and,type,
op_and: $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff('#skF_40',type,
'#skF_40': $i ).
tff('#skF_48',type,
'#skF_48': $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_37',type,
'#skF_37': $i ).
tff(and_3,type,
and_3: $o ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(op_implies_and,type,
op_implies_and: $o ).
tff(op_strict_implies,type,
op_strict_implies: $o ).
tff('#skF_71',type,
'#skF_71': $i ).
tff(equivalence_1,type,
equivalence_1: $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(kn2,type,
kn2: $o ).
tff('#skF_16',type,
'#skF_16': $i ).
tff('#skF_85',type,
'#skF_85': $i ).
tff(equivalence_3,type,
equivalence_3: $o ).
tff(and_1,type,
and_1: $o ).
tff('#skF_47',type,
'#skF_47': $i ).
tff('#skF_92',type,
'#skF_92': $i ).
tff('#skF_65',type,
'#skF_65': $i ).
tff(cn1,type,
cn1: $o ).
tff('#skF_26',type,
'#skF_26': $i ).
tff('#skF_81',type,
'#skF_81': $i ).
tff(necessitation,type,
necessitation: $o ).
tff('#skF_53',type,
'#skF_53': $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_51',type,
'#skF_51': $i ).
tff(or_1,type,
or_1: $o ).
tff(implies_3,type,
implies_3: $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_45',type,
'#skF_45': $i ).
tff(axiom_s4,type,
axiom_s4: $o ).
tff('#skF_46',type,
'#skF_46': $i ).
tff('#skF_39',type,
'#skF_39': $i ).
tff(or,type,
or: ( $i * $i ) > $i ).
tff(modus_tollens,type,
modus_tollens: $o ).
tff('#skF_72',type,
'#skF_72': $i ).
tff(r2,type,
r2: $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(not,type,
not: $i > $i ).
tff('#skF_61',type,
'#skF_61': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_68',type,
'#skF_68': $i ).
tff(axiom_m2,type,
axiom_m2: $o ).
tff(modus_ponens,type,
modus_ponens: $o ).
tff('#skF_82',type,
'#skF_82': $i ).
tff('#skF_84',type,
'#skF_84': $i ).
tff(op_or,type,
op_or: $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(substitution_of_equivalents,type,
substitution_of_equivalents: $o ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(axiom_s3,type,
axiom_s3: $o ).
tff(substitution_strict_equiv,type,
substitution_strict_equiv: $o ).
tff(axiom_M,type,
axiom_M: $o ).
tff(strict_implies,type,
strict_implies: ( $i * $i ) > $i ).
tff('#skF_89',type,
'#skF_89': $i ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(necessarily,type,
necessarily: $i > $i ).
tff(axiom_m4,type,
axiom_m4: $o ).
tff('#skF_64',type,
'#skF_64': $i ).
tff(op_equiv,type,
op_equiv: $o ).
tff('#skF_50',type,
'#skF_50': $i ).
tff('#skF_90',type,
'#skF_90': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff(modus_ponens_strict_implies,type,
modus_ponens_strict_implies: $o ).
tff(axiom_m7,type,
axiom_m7: $o ).
tff('#skF_42',type,
'#skF_42': $i ).
tff(axiom_s2,type,
axiom_s2: $o ).
tff('#skF_77',type,
'#skF_77': $i ).
tff(or_3,type,
or_3: $o ).
tff(op_necessarily,type,
op_necessarily: $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(strict_equiv,type,
strict_equiv: ( $i * $i ) > $i ).
tff('#skF_93',type,
'#skF_93': $i ).
tff(kn1,type,
kn1: $o ).
tff(axiom_m6,type,
axiom_m6: $o ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_35',type,
'#skF_35': $i ).
tff('#skF_70',type,
'#skF_70': $i ).
tff('#skF_66',type,
'#skF_66': $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(and,type,
and: ( $i * $i ) > $i ).
tff('#skF_63',type,
'#skF_63': $i ).
tff(axiom_m1,type,
axiom_m1: $o ).
tff('#skF_88',type,
'#skF_88': $i ).
tff(implies_1,type,
implies_1: $o ).
tff('#skF_44',type,
'#skF_44': $i ).
tff('#skF_83',type,
'#skF_83': $i ).
tff(axiom_m10,type,
axiom_m10: $o ).
tff(op_implies,type,
op_implies: $o ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff('#skF_59',type,
'#skF_59': $i ).
tff(axiom_m9,type,
axiom_m9: $o ).
tff('#skF_73',type,
'#skF_73': $i ).
tff('#skF_91',type,
'#skF_91': $i ).
tff(cn3,type,
cn3: $o ).
tff(or_2,type,
or_2: $o ).
tff('#skF_58',type,
'#skF_58': $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(axiom_m5,type,
axiom_m5: $o ).
tff('#skF_62',type,
'#skF_62': $i ).
tff('#skF_34',type,
'#skF_34': $i ).
tff('#skF_75',type,
'#skF_75': $i ).
tff('#skF_74',type,
'#skF_74': $i ).
tff(f_250,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
tff(f_76,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_1) ).
tff(f_251,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
tff(f_80,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
tff(f_247,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
tff(f_60,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_483,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
tff(f_437,axiom,
( op_strict_implies
=> ! [X,Y] : ( strict_implies(X,Y) = necessarily(implies(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
tff(f_472,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).
tff(f_297,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
tff(f_485,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
tff(f_441,axiom,
( op_strict_equiv
=> ! [X,Y] : ( strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_equiv) ).
tff(f_255,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
tff(f_96,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_3) ).
tff(f_374,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
tff(f_475,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_axiom_M) ).
tff(f_328,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
tff(f_125,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
tff(f_476,axiom,
axiom_5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_axiom_5) ).
tff(f_340,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_5) ).
tff(f_484,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_equiv) ).
tff(f_214,axiom,
( op_equiv
=> ! [X,Y] : ( equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
tff(f_313,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(Y) )
=> is_a_theorem(and(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',adjunction) ).
tff(f_264,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',substitution_of_equivalents) ).
tff(f_67,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
tff(f_480,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_possibly) ).
tff(f_429,axiom,
( op_possibly
=> ! [X] : ( possibly(X) = not(necessarily(not(X))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
tff(f_481,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
tff(f_244,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
tff(f_206,axiom,
( op_implies_and
=> ! [X,Y] : ( implies(X,Y) = not(and(X,not(Y))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
tff(f_198,axiom,
( op_or
=> ! [X,Y] : ( or(X,Y) = not(and(not(X),not(Y))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
tff(f_256,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).
tff(f_100,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_1) ).
tff(f_258,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
tff(f_108,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_3) ).
tff(f_151,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
tff(f_146,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn3) ).
tff(f_249,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
tff(f_72,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
tff(f_254,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
tff(f_92,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_2) ).
tff(f_488,negated_conjecture,
~ axiom_m9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
tff(f_395,axiom,
( axiom_m9
<=> ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m9) ).
tff(c_132,plain,
implies_1,
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_22,plain,
! [X_7,Y_8] :
( is_a_theorem(implies(X_7,implies(Y_8,X_7)))
| ~ implies_1 ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_390,plain,
! [X_7,Y_8] : is_a_theorem(implies(X_7,implies(Y_8,X_7))),
inference(demodulation,[status(thm),theory(equality)],[c_132,c_22]) ).
tff(c_134,plain,
implies_2,
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_26,plain,
! [X_9,Y_10] :
( is_a_theorem(implies(implies(X_9,implies(X_9,Y_10)),implies(X_9,Y_10)))
| ~ implies_2 ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_51370,plain,
! [X_4115,Y_4116] : is_a_theorem(implies(implies(X_4115,implies(X_4115,Y_4116)),implies(X_4115,Y_4116))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_128,plain,
modus_ponens,
inference(cnfTransformation,[status(thm)],[f_247]) ).
tff(c_2,plain,
! [Y_2,X_1] :
( is_a_theorem(Y_2)
| ~ is_a_theorem(implies(X_1,Y_2))
| ~ is_a_theorem(X_1)
| ~ modus_ponens ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_405,plain,
! [Y_2,X_1] :
( is_a_theorem(Y_2)
| ~ is_a_theorem(implies(X_1,Y_2))
| ~ is_a_theorem(X_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_53285,plain,
! [X_4262,Y_4263] :
( is_a_theorem(implies(X_4262,Y_4263))
| ~ is_a_theorem(implies(X_4262,implies(X_4262,Y_4263))) ),
inference(resolution,[status(thm)],[c_51370,c_405]) ).
tff(c_53350,plain,
! [Y_8] : is_a_theorem(implies(Y_8,Y_8)),
inference(resolution,[status(thm)],[c_390,c_53285]) ).
tff(c_286,plain,
op_strict_implies,
inference(cnfTransformation,[status(thm)],[f_483]) ).
tff(c_266,plain,
! [X_107,Y_108] :
( ( necessarily(implies(X_107,Y_108)) = strict_implies(X_107,Y_108) )
| ~ op_strict_implies ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_50594,plain,
! [X_4030,Y_4031] : ( necessarily(implies(X_4030,Y_4031)) = strict_implies(X_4030,Y_4031) ),
inference(demodulation,[status(thm),theory(equality)],[c_286,c_266]) ).
tff(c_272,plain,
necessitation,
inference(cnfTransformation,[status(thm)],[f_472]) ).
tff(c_158,plain,
! [X_66] :
( is_a_theorem(necessarily(X_66))
| ~ is_a_theorem(X_66)
| ~ necessitation ),
inference(cnfTransformation,[status(thm)],[f_297]) ).
tff(c_318,plain,
! [X_66] :
( is_a_theorem(necessarily(X_66))
| ~ is_a_theorem(X_66) ),
inference(demodulation,[status(thm),theory(equality)],[c_272,c_158]) ).
tff(c_50603,plain,
! [X_4030,Y_4031] :
( is_a_theorem(strict_implies(X_4030,Y_4031))
| ~ is_a_theorem(implies(X_4030,Y_4031)) ),
inference(superposition,[status(thm),theory(equality)],[c_50594,c_318]) ).
tff(c_290,plain,
op_strict_equiv,
inference(cnfTransformation,[status(thm)],[f_485]) ).
tff(c_268,plain,
! [X_109,Y_110] :
( ( and(strict_implies(X_109,Y_110),strict_implies(Y_110,X_109)) = strict_equiv(X_109,Y_110) )
| ~ op_strict_equiv ),
inference(cnfTransformation,[status(thm)],[f_441]) ).
tff(c_51415,plain,
! [X_4120,Y_4121] : ( and(strict_implies(X_4120,Y_4121),strict_implies(Y_4121,X_4120)) = strict_equiv(X_4120,Y_4121) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_268]) ).
tff(c_142,plain,
and_3,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_42,plain,
! [X_18,Y_19] :
( is_a_theorem(implies(X_18,implies(Y_19,and(X_18,Y_19))))
| ~ and_3 ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_364,plain,
! [X_18,Y_19] : is_a_theorem(implies(X_18,implies(Y_19,and(X_18,Y_19)))),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_42]) ).
tff(c_48137,plain,
! [X_3803,Y_3804] : is_a_theorem(implies(implies(X_3803,implies(X_3803,Y_3804)),implies(X_3803,Y_3804))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_49414,plain,
! [X_3910,Y_3911] :
( is_a_theorem(implies(X_3910,Y_3911))
| ~ is_a_theorem(implies(X_3910,implies(X_3910,Y_3911))) ),
inference(resolution,[status(thm)],[c_48137,c_405]) ).
tff(c_49474,plain,
! [Y_19] : is_a_theorem(implies(Y_19,and(Y_19,Y_19))),
inference(resolution,[status(thm)],[c_364,c_49414]) ).
tff(c_47183,plain,
! [X_3698,Y_3699] : ( necessarily(implies(X_3698,Y_3699)) = strict_implies(X_3698,Y_3699) ),
inference(demodulation,[status(thm),theory(equality)],[c_286,c_266]) ).
tff(c_47745,plain,
! [X_3774,Y_3775] :
( is_a_theorem(strict_implies(X_3774,Y_3775))
| ~ is_a_theorem(implies(X_3774,Y_3775)) ),
inference(superposition,[status(thm),theory(equality)],[c_47183,c_318]) ).
tff(c_234,plain,
( axiom_m4
| ~ is_a_theorem(strict_implies('#skF_84',and('#skF_84','#skF_84'))) ),
inference(cnfTransformation,[status(thm)],[f_374]) ).
tff(c_47182,plain,
~ is_a_theorem(strict_implies('#skF_84',and('#skF_84','#skF_84'))),
inference(splitLeft,[status(thm)],[c_234]) ).
tff(c_47770,plain,
~ is_a_theorem(implies('#skF_84',and('#skF_84','#skF_84'))),
inference(resolution,[status(thm)],[c_47745,c_47182]) ).
tff(c_49521,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_49474,c_47770]) ).
tff(c_49522,plain,
axiom_m4,
inference(splitRight,[status(thm)],[c_234]) ).
tff(c_236,plain,
! [X_94] :
( is_a_theorem(strict_implies(X_94,and(X_94,X_94)))
| ~ axiom_m4 ),
inference(cnfTransformation,[status(thm)],[f_374]) ).
tff(c_49557,plain,
! [X_94] : is_a_theorem(strict_implies(X_94,and(X_94,X_94))),
inference(demodulation,[status(thm),theory(equality)],[c_49522,c_236]) ).
tff(c_49561,plain,
! [X_3919,Y_3920] : ( necessarily(implies(X_3919,Y_3920)) = strict_implies(X_3919,Y_3920) ),
inference(demodulation,[status(thm),theory(equality)],[c_286,c_266]) ).
tff(c_276,plain,
axiom_M,
inference(cnfTransformation,[status(thm)],[f_475]) ).
tff(c_192,plain,
! [X_75] :
( is_a_theorem(implies(necessarily(X_75),X_75))
| ~ axiom_M ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_308,plain,
! [X_75] : is_a_theorem(implies(necessarily(X_75),X_75)),
inference(demodulation,[status(thm),theory(equality)],[c_276,c_192]) ).
tff(c_50277,plain,
! [X_3999,Y_4000] : is_a_theorem(implies(strict_implies(X_3999,Y_4000),implies(X_3999,Y_4000))),
inference(superposition,[status(thm),theory(equality)],[c_49561,c_308]) ).
tff(c_50534,plain,
! [X_4027,Y_4028] :
( is_a_theorem(implies(X_4027,Y_4028))
| ~ is_a_theorem(strict_implies(X_4027,Y_4028)) ),
inference(resolution,[status(thm)],[c_50277,c_405]) ).
tff(c_50580,plain,
! [X_94] : is_a_theorem(implies(X_94,and(X_94,X_94))),
inference(resolution,[status(thm)],[c_49557,c_50534]) ).
tff(c_70,plain,
! [P_33] :
( is_a_theorem(implies(P_33,and(P_33,P_33)))
| ~ kn1 ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_49560,plain,
~ kn1,
inference(splitLeft,[status(thm)],[c_70]) ).
tff(c_68,plain,
( kn1
| ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_49580,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(negUnitSimplification,[status(thm)],[c_49560,c_68]) ).
tff(c_50585,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50580,c_49580]) ).
tff(c_50586,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_51467,plain,
! [Y_4122] : is_a_theorem(implies(strict_implies(Y_4122,Y_4122),strict_equiv(Y_4122,Y_4122))),
inference(superposition,[status(thm),theory(equality)],[c_51415,c_50586]) ).
tff(c_51510,plain,
! [Y_4130] :
( is_a_theorem(strict_equiv(Y_4130,Y_4130))
| ~ is_a_theorem(strict_implies(Y_4130,Y_4130)) ),
inference(resolution,[status(thm)],[c_51467,c_405]) ).
tff(c_51519,plain,
! [Y_4031] :
( is_a_theorem(strict_equiv(Y_4031,Y_4031))
| ~ is_a_theorem(implies(Y_4031,Y_4031)) ),
inference(resolution,[status(thm)],[c_50603,c_51510]) ).
tff(c_53354,plain,
! [Y_4031] : is_a_theorem(strict_equiv(Y_4031,Y_4031)),
inference(demodulation,[status(thm),theory(equality)],[c_53350,c_51519]) ).
tff(c_278,plain,
axiom_5,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_204,plain,
! [X_78] :
( is_a_theorem(implies(possibly(X_78),necessarily(possibly(X_78))))
| ~ axiom_5 ),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_304,plain,
! [X_78] : is_a_theorem(implies(possibly(X_78),necessarily(possibly(X_78)))),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_204]) ).
tff(c_288,plain,
op_equiv,
inference(cnfTransformation,[status(thm)],[f_484]) ).
tff(c_120,plain,
! [X_64,Y_65] :
( ( and(implies(X_64,Y_65),implies(Y_65,X_64)) = equiv(X_64,Y_65) )
| ~ op_equiv ),
inference(cnfTransformation,[status(thm)],[f_214]) ).
tff(c_51607,plain,
! [X_4139,Y_4140] : ( and(implies(X_4139,Y_4140),implies(Y_4140,X_4139)) = equiv(X_4139,Y_4140) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_120]) ).
tff(c_176,plain,
( is_a_theorem('#skF_60')
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_36619,plain,
adjunction,
inference(splitLeft,[status(thm)],[c_176]) ).
tff(c_172,plain,
! [X_69,Y_70] :
( is_a_theorem(and(X_69,Y_70))
| ~ is_a_theorem(Y_70)
| ~ is_a_theorem(X_69)
| ~ adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_51176,plain,
! [X_69,Y_70] :
( is_a_theorem(and(X_69,Y_70))
| ~ is_a_theorem(Y_70)
| ~ is_a_theorem(X_69) ),
inference(demodulation,[status(thm),theory(equality)],[c_36619,c_172]) ).
tff(c_56511,plain,
! [X_4418,Y_4419] :
( is_a_theorem(equiv(X_4418,Y_4419))
| ~ is_a_theorem(implies(Y_4419,X_4418))
| ~ is_a_theorem(implies(X_4418,Y_4419)) ),
inference(superposition,[status(thm),theory(equality)],[c_51607,c_51176]) ).
tff(c_56591,plain,
! [X_78] :
( is_a_theorem(equiv(necessarily(possibly(X_78)),possibly(X_78)))
| ~ is_a_theorem(implies(necessarily(possibly(X_78)),possibly(X_78))) ),
inference(resolution,[status(thm)],[c_304,c_56511]) ).
tff(c_57836,plain,
! [X_4442] : is_a_theorem(equiv(necessarily(possibly(X_4442)),possibly(X_4442))),
inference(demodulation,[status(thm),theory(equality)],[c_308,c_56591]) ).
tff(c_156,plain,
substitution_of_equivalents,
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_10,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ is_a_theorem(equiv(X_3,Y_4))
| ~ substitution_of_equivalents ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_400,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ is_a_theorem(equiv(X_3,Y_4)) ),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_10]) ).
tff(c_57875,plain,
! [X_4442] : ( necessarily(possibly(X_4442)) = possibly(X_4442) ),
inference(resolution,[status(thm)],[c_57836,c_400]) ).
tff(c_280,plain,
op_possibly,
inference(cnfTransformation,[status(thm)],[f_480]) ).
tff(c_262,plain,
! [X_105] :
( ( not(necessarily(not(X_105))) = possibly(X_105) )
| ~ op_possibly ),
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_299,plain,
! [X_105] : ( not(necessarily(not(X_105))) = possibly(X_105) ),
inference(demodulation,[status(thm),theory(equality)],[c_280,c_262]) ).
tff(c_282,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_481]) ).
tff(c_124,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_116,plain,
! [X_60,Y_61] :
( ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) )
| ~ op_implies_and ),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_324,plain,
! [X_60,Y_61] : ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_112,plain,
! [X_56,Y_57] :
( ( not(and(not(X_56),not(Y_57))) = or(X_56,Y_57) )
| ~ op_or ),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_326,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_282,c_324,c_112]) ).
tff(c_144,plain,
or_1,
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_46,plain,
! [X_20,Y_21] :
( is_a_theorem(implies(X_20,or(X_20,Y_21)))
| ~ or_1 ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_357,plain,
! [X_20,Y_21] : is_a_theorem(implies(X_20,or(X_20,Y_21))),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_46]) ).
tff(c_42271,plain,
! [X_3333,Y_3334] : is_a_theorem(implies(implies(X_3333,implies(X_3333,Y_3334)),implies(X_3333,Y_3334))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_43863,plain,
! [X_3451,Y_3452] :
( is_a_theorem(implies(X_3451,Y_3452))
| ~ is_a_theorem(implies(X_3451,implies(X_3451,Y_3452))) ),
inference(resolution,[status(thm)],[c_42271,c_405]) ).
tff(c_43928,plain,
! [Y_8] : is_a_theorem(implies(Y_8,Y_8)),
inference(resolution,[status(thm)],[c_390,c_43863]) ).
tff(c_148,plain,
or_3,
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_54,plain,
! [X_24,Z_26,Y_25] :
( is_a_theorem(implies(implies(X_24,Z_26),implies(implies(Y_25,Z_26),implies(or(X_24,Y_25),Z_26))))
| ~ or_3 ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_346,plain,
! [X_24,Z_26,Y_25] : is_a_theorem(implies(implies(X_24,Z_26),implies(implies(Y_25,Z_26),implies(or(X_24,Y_25),Z_26)))),
inference(demodulation,[status(thm),theory(equality)],[c_148,c_54]) ).
tff(c_44320,plain,
! [Y_3469,Z_3470] : is_a_theorem(implies(implies(Y_3469,Z_3470),implies(or(Y_3469,Y_3469),Z_3470))),
inference(resolution,[status(thm)],[c_346,c_43863]) ).
tff(c_46347,plain,
! [Y_3603,Z_3604] :
( is_a_theorem(implies(or(Y_3603,Y_3603),Z_3604))
| ~ is_a_theorem(implies(Y_3603,Z_3604)) ),
inference(resolution,[status(thm)],[c_44320,c_405]) ).
tff(c_92,plain,
( r1
| ~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_36656,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(splitLeft,[status(thm)],[c_92]) ).
tff(c_46360,plain,
~ is_a_theorem(implies('#skF_45','#skF_45')),
inference(resolution,[status(thm)],[c_46347,c_36656]) ).
tff(c_46386,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_43928,c_46360]) ).
tff(c_46387,plain,
r1,
inference(splitRight,[status(thm)],[c_92]) ).
tff(c_94,plain,
! [P_45] :
( is_a_theorem(implies(or(P_45,P_45),P_45))
| ~ r1 ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_46390,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(demodulation,[status(thm),theory(equality)],[c_46387,c_94]) ).
tff(c_88,plain,
( cn3
| ~ is_a_theorem(implies(implies(not('#skF_44'),'#skF_44'),'#skF_44')) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_328,plain,
( cn3
| ~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')) ),
inference(demodulation,[status(thm),theory(equality)],[c_326,c_88]) ).
tff(c_36651,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(splitLeft,[status(thm)],[c_328]) ).
tff(c_46394,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_46390,c_36651]) ).
tff(c_46395,plain,
cn3,
inference(splitRight,[status(thm)],[c_328]) ).
tff(c_90,plain,
! [P_44] :
( is_a_theorem(implies(implies(not(P_44),P_44),P_44))
| ~ cn3 ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_327,plain,
! [P_44] :
( is_a_theorem(implies(or(P_44,P_44),P_44))
| ~ cn3 ),
inference(demodulation,[status(thm),theory(equality)],[c_326,c_90]) ).
tff(c_46405,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(demodulation,[status(thm),theory(equality)],[c_46395,c_327]) ).
tff(c_46401,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(splitLeft,[status(thm)],[c_92]) ).
tff(c_46409,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_46405,c_46401]) ).
tff(c_46410,plain,
r1,
inference(splitRight,[status(thm)],[c_92]) ).
tff(c_47177,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(demodulation,[status(thm),theory(equality)],[c_46410,c_94]) ).
tff(c_56595,plain,
! [P_45] :
( is_a_theorem(equiv(P_45,or(P_45,P_45)))
| ~ is_a_theorem(implies(P_45,or(P_45,P_45))) ),
inference(resolution,[status(thm)],[c_47177,c_56511]) ).
tff(c_56669,plain,
! [P_4420] : is_a_theorem(equiv(P_4420,or(P_4420,P_4420))),
inference(demodulation,[status(thm),theory(equality)],[c_357,c_56595]) ).
tff(c_56703,plain,
! [P_4420] : ( or(P_4420,P_4420) = P_4420 ),
inference(resolution,[status(thm)],[c_56669,c_400]) ).
tff(c_50960,plain,
! [X_4076,Y_4077] : ( not(and(X_4076,not(Y_4077))) = implies(X_4076,Y_4077) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_54368,plain,
! [X_4317,X_4318,Y_4319] : ( implies(X_4317,and(X_4318,not(Y_4319))) = not(and(X_4317,implies(X_4318,Y_4319))) ),
inference(superposition,[status(thm),theory(equality)],[c_50960,c_324]) ).
tff(c_54516,plain,
! [Y_4319] : is_a_theorem(not(and(not(Y_4319),implies(not(Y_4319),Y_4319)))),
inference(superposition,[status(thm),theory(equality)],[c_54368,c_50586]) ).
tff(c_54575,plain,
! [Y_4319] : is_a_theorem(not(and(not(Y_4319),or(Y_4319,Y_4319)))),
inference(demodulation,[status(thm),theory(equality)],[c_326,c_54516]) ).
tff(c_56887,plain,
! [Y_4423] : is_a_theorem(not(and(not(Y_4423),Y_4423))),
inference(demodulation,[status(thm),theory(equality)],[c_56703,c_54575]) ).
tff(c_56903,plain,
! [Y_61] : is_a_theorem(implies(not(not(Y_61)),Y_61)),
inference(superposition,[status(thm),theory(equality)],[c_324,c_56887]) ).
tff(c_56910,plain,
! [Y_61] : is_a_theorem(or(not(Y_61),Y_61)),
inference(demodulation,[status(thm),theory(equality)],[c_326,c_56903]) ).
tff(c_56911,plain,
! [Y_4424] : is_a_theorem(or(not(Y_4424),Y_4424)),
inference(demodulation,[status(thm),theory(equality)],[c_326,c_56903]) ).
tff(c_130,plain,
modus_tollens,
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_18,plain,
! [Y_6,X_5] :
( is_a_theorem(implies(implies(not(Y_6),not(X_5)),implies(X_5,Y_6)))
| ~ modus_tollens ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_51312,plain,
! [Y_4113,X_4114] : is_a_theorem(implies(or(Y_4113,not(X_4114)),implies(X_4114,Y_4113))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_326,c_18]) ).
tff(c_51325,plain,
! [X_4114,Y_4113] :
( is_a_theorem(implies(X_4114,Y_4113))
| ~ is_a_theorem(or(Y_4113,not(X_4114))) ),
inference(resolution,[status(thm)],[c_51312,c_405]) ).
tff(c_56937,plain,
! [X_4425] : is_a_theorem(implies(X_4425,not(not(X_4425)))),
inference(resolution,[status(thm)],[c_56911,c_51325]) ).
tff(c_51616,plain,
! [X_4139,Y_4140] :
( is_a_theorem(equiv(X_4139,Y_4140))
| ~ is_a_theorem(implies(Y_4140,X_4139))
| ~ is_a_theorem(implies(X_4139,Y_4140)) ),
inference(superposition,[status(thm),theory(equality)],[c_51607,c_51176]) ).
tff(c_56939,plain,
! [X_4425] :
( is_a_theorem(equiv(not(not(X_4425)),X_4425))
| ~ is_a_theorem(implies(not(not(X_4425)),X_4425)) ),
inference(resolution,[status(thm)],[c_56937,c_51616]) ).
tff(c_57032,plain,
! [X_4430] : is_a_theorem(equiv(not(not(X_4430)),X_4430)),
inference(demodulation,[status(thm),theory(equality)],[c_56910,c_326,c_56939]) ).
tff(c_57077,plain,
! [X_4431] : ( not(not(X_4431)) = X_4431 ),
inference(resolution,[status(thm)],[c_57032,c_400]) ).
tff(c_57302,plain,
! [X_105] : ( not(possibly(X_105)) = necessarily(not(X_105)) ),
inference(superposition,[status(thm),theory(equality)],[c_299,c_57077]) ).
tff(c_36628,plain,
! [X_2733] : ( not(necessarily(not(X_2733))) = possibly(X_2733) ),
inference(demodulation,[status(thm),theory(equality)],[c_280,c_262]) ).
tff(c_36631,plain,
! [X_2733] : ( possibly(necessarily(not(X_2733))) = not(necessarily(possibly(X_2733))) ),
inference(superposition,[status(thm),theory(equality)],[c_36628,c_299]) ).
tff(c_57886,plain,
! [X_2733] : ( possibly(necessarily(not(X_2733))) = not(possibly(X_2733)) ),
inference(demodulation,[status(thm),theory(equality)],[c_57875,c_36631]) ).
tff(c_59652,plain,
! [X_4479] : ( possibly(necessarily(not(X_4479))) = necessarily(not(X_4479)) ),
inference(demodulation,[status(thm),theory(equality)],[c_57302,c_57886]) ).
tff(c_59740,plain,
! [X_105] : ( necessarily(not(necessarily(not(X_105)))) = possibly(necessarily(possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_299,c_59652]) ).
tff(c_59768,plain,
! [X_105] : ( possibly(possibly(X_105)) = possibly(X_105) ),
inference(demodulation,[status(thm),theory(equality)],[c_57875,c_57875,c_299,c_59740]) ).
tff(c_140,plain,
and_2,
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_38,plain,
! [X_16,Y_17] :
( is_a_theorem(implies(and(X_16,Y_17),Y_17))
| ~ and_2 ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_368,plain,
! [X_16,Y_17] : is_a_theorem(implies(and(X_16,Y_17),Y_17)),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_38]) ).
tff(c_51005,plain,
! [Y_4081,X_4082] :
( is_a_theorem(Y_4081)
| ~ is_a_theorem(implies(X_4082,Y_4081))
| ~ is_a_theorem(X_4082) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_51050,plain,
! [Y_17,X_16] :
( is_a_theorem(Y_17)
| ~ is_a_theorem(and(X_16,Y_17)) ),
inference(resolution,[status(thm)],[c_368,c_51005]) ).
tff(c_51697,plain,
! [Y_4145,X_4146] :
( is_a_theorem(strict_implies(Y_4145,X_4146))
| ~ is_a_theorem(strict_equiv(X_4146,Y_4145)) ),
inference(superposition,[status(thm),theory(equality)],[c_51415,c_51050]) ).
tff(c_292,plain,
~ axiom_m9,
inference(cnfTransformation,[status(thm)],[f_488]) ).
tff(c_254,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly('#skF_93')),possibly('#skF_93'))) ),
inference(cnfTransformation,[status(thm)],[f_395]) ).
tff(c_300,plain,
~ is_a_theorem(strict_implies(possibly(possibly('#skF_93')),possibly('#skF_93'))),
inference(negUnitSimplification,[status(thm)],[c_292,c_254]) ).
tff(c_51733,plain,
~ is_a_theorem(strict_equiv(possibly('#skF_93'),possibly(possibly('#skF_93')))),
inference(resolution,[status(thm)],[c_51697,c_300]) ).
tff(c_59771,plain,
~ is_a_theorem(strict_equiv(possibly('#skF_93'),possibly('#skF_93'))),
inference(demodulation,[status(thm),theory(equality)],[c_59768,c_51733]) ).
tff(c_59779,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_53354,c_59771]) ).
tff(c_59781,plain,
~ adjunction,
inference(splitRight,[status(thm)],[c_176]) ).
tff(c_178,plain,
( is_a_theorem('#skF_59')
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_59784,plain,
is_a_theorem('#skF_59'),
inference(negUnitSimplification,[status(thm)],[c_59781,c_178]) ).
tff(c_59780,plain,
is_a_theorem('#skF_60'),
inference(splitRight,[status(thm)],[c_176]) ).
tff(c_60836,plain,
! [X_4617,Y_4618] : is_a_theorem(implies(X_4617,implies(Y_4618,and(X_4617,Y_4618)))),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_42]) ).
tff(c_60949,plain,
! [Y_4632,X_4633] :
( is_a_theorem(implies(Y_4632,and(X_4633,Y_4632)))
| ~ is_a_theorem(X_4633) ),
inference(resolution,[status(thm)],[c_60836,c_405]) ).
tff(c_61328,plain,
! [X_4661,Y_4662] :
( is_a_theorem(and(X_4661,Y_4662))
| ~ is_a_theorem(Y_4662)
| ~ is_a_theorem(X_4661) ),
inference(resolution,[status(thm)],[c_60949,c_405]) ).
tff(c_174,plain,
( ~ is_a_theorem(and('#skF_59','#skF_60'))
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_59787,plain,
~ is_a_theorem(and('#skF_59','#skF_60')),
inference(negUnitSimplification,[status(thm)],[c_59781,c_174]) ).
tff(c_61343,plain,
( ~ is_a_theorem('#skF_60')
| ~ is_a_theorem('#skF_59') ),
inference(resolution,[status(thm)],[c_61328,c_59787]) ).
tff(c_61354,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_59784,c_59780,c_61343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : LCL535+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 14:37:14 EDT 2023
% 0.15/0.37 % CPUTime :
% 28.81/13.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.81/13.87
% 28.81/13.87 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.81/13.93
% 28.81/13.93 Inference rules
% 28.81/13.93 ----------------------
% 28.81/13.93 #Ref : 0
% 28.81/13.93 #Sup : 14630
% 28.81/13.93 #Fact : 0
% 28.81/13.93 #Define : 0
% 28.81/13.93 #Split : 810
% 28.81/13.93 #Chain : 0
% 28.81/13.93 #Close : 0
% 28.81/13.93
% 28.81/13.93 Ordering : KBO
% 28.81/13.93
% 28.81/13.93 Simplification rules
% 28.81/13.93 ----------------------
% 28.81/13.93 #Subsume : 2038
% 28.81/13.93 #Demod : 8076
% 28.81/13.93 #Tautology : 3271
% 28.81/13.93 #SimpNegUnit : 191
% 28.81/13.93 #BackRed : 189
% 28.81/13.93
% 28.81/13.93 #Partial instantiations: 0
% 28.81/13.93 #Strategies tried : 1
% 28.81/13.93
% 28.81/13.93 Timing (in seconds)
% 28.81/13.93 ----------------------
% 28.81/13.93 Preprocessing : 0.73
% 28.81/13.93 Parsing : 0.36
% 28.81/13.93 CNF conversion : 0.06
% 28.81/13.93 Main loop : 12.09
% 28.81/13.93 Inferencing : 3.26
% 28.81/13.93 Reduction : 5.42
% 28.81/13.93 Demodulation : 3.75
% 28.81/13.93 BG Simplification : 0.13
% 28.81/13.93 Subsumption : 2.52
% 28.81/13.93 Abstraction : 0.16
% 28.81/13.93 MUC search : 0.00
% 28.81/13.93 Cooper : 0.00
% 28.81/13.93 Total : 12.91
% 28.81/13.93 Index Insertion : 0.00
% 28.81/13.93 Index Deletion : 0.00
% 28.81/13.93 Index Matching : 0.00
% 28.81/13.93 BG Taut test : 0.00
%------------------------------------------------------------------------------